Q: Two cylinders fitted with pistons contains equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of gas in B is
(a) 30 K
(b) 18 K
(c) 50 K
(d) 42 K
Solution :(d)
In cylinder A heat is supplied at constant pressure while in cylinder B heat is supplied at constan volume.
 (ΔQ)A = nCP (ΔT)A and (ΔQ)B = nCV (ΔT)B
Given that (ΔQ)A = (ΔQ)B
(ΔT)B = Cp/Cv(ΔT)A
= (1.4) (30) (Since Cp/Cv = 1.4)
= 42 K

Q: Two cylinders P and Q have the same length and diameter and are made of different materials having thermal conductivities in the ratio 2 : 3. These two cylinders are combined to make a cylinder. One end of P is kept at 100° C and another end of Q at 0°C. The temperature at the interface of P and Q is
(a) 30°C
(b) 40°C
(c) 50°C
(d) 60°C
Solution : (b) Let temperature at interface is θ
k1(100-θ) = k2(θ-0)
Here , k1/k2 = 2/3
By solving , θ = 40°C